a motor oil retailer needs to fill 40 one quart bottles, and he has two tanks: one tank contains 2 gallons and the other contains 12 which will he need to fill the bottles.?

Using Cramer's rule, the solution to the system of equations is given as follows:

x = -10, y = 9.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

There are multiple ways to solve a system of equations, and one of them is Cramer's Rule, in which we use the determinants of matrices to find the solutions.

In the context of this problem, the system is:

The matrix for the system is:

[tex]M = \left[\begin{array}{cc}1&2\\-3&-2\end{array}\right][/tex]

Hence it's determinant is:

|M| = 1(-2) - (-3)(2) = -2 + 6 = 4.

The matrix for x is given by:

[tex]M_x = \left[\begin{array}{cc}8&2\\12&-2\end{array}\right][/tex]

Hence it's determinant is:

|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.

The matrix for y is given by:

[tex]M_y = \left[\begin{array}{cc}1&8\\-3&12\end{array}\right][/tex]

Hence it's determinant is:

|My| =  12 - (-3)(8) = 12 + 24 = 36.

Then the solutions are given as follows:

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Answer:

150

Step-by-step explanation:

Answer:

Question 1:

x + y = 97

$1.55x + $1.09y = $120.45

Question 2:

32

Question 3:

65

Step-by-step explanation:

phew, way to long to explain why. A brainliest would be nice :)

Answer:

1/6 chance

Step-by-step explanation:

All the identifiers that are included when identifying significant digits are-

Each of the digits of a number starting with the digit farthest to a left that is not zero as well as ending with the digit farthest to a right that is neither zero or is a zero but is considered exact.

For the given options.

Except option 1 every option is correct.

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Answer:

a. 4.67 dollars per hour

b. 0.43 minutes per page

Explanation:

Part a.

To know the cost per hour of bike use, we need to divide the total cost by the number of hours, so:

So, the cost is 4.67 dollars per hour

Part b.

In the same way, the number of minutes per page can be calculated as the division of the number of minutes by the number of pages, so:

So, it takes 0.43 minutes per page.

Given the fraction below

To simplify the above fraction, we will divide both the numerato

So we need to solve the following equation for x:

We can apply a square root to both sides but it is important to remember the following property. For any given number a we have:

Which means that:

So for our case we have:

Then the solutions are 7 and -7.

Answer:

Step-by-step explanation:

The first thing you need to do, is find the total amount of gorillas.
to do this, you are going to use the equation:

24 + g = 7g

Both sides are equal, since the wallabies and the buffalo are equal. This makes the equation true.
you subtract g from 7g, and you should get:

24= 6g

Divide by six:

4 = g  

That is the # of gorillas.

Now, if you add 24 + 4

You get the # of buffalo.

Which is: 28

Since the buffalo and wallabies are the same, the # of wallabies is also 28.
if you want to check, multiply 4x7 to get the amount of wallabies.

Explanation

Lets first find the slope:

Now let's use the point-slope formula:

Answer

The number of different committees that can be formed is 34,650.

First, we know that there are 11 teachers and the committee needs to have two teachers, so let's find the number of combinations here.

Remember that if we have a set of N elements and we need to select K of these, the number of different selections is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case we would have N = 11 and K = 2, so we get:

[tex]C(11, 2) = \frac{11!}{(11 - 2)!*2!} = \frac{11*10}{2} = 11*5 = 55[/tex]

There are 55 combinations.

For the students we do the same thing, here we have 36 students and we need to select two, so:

[tex]C(36, 2) = \frac{36!}{(36 - 2)!*2!} = \frac{36*35}{2} = 630[/tex]

So we have 55 combinations for the teachers and 630 for the students, then the total number of different committees is:

C = 630*55 = 34,650

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a . After stopping for lunch Elena has travelled 50 miles.

b . She is less than 9 / 10 to her grand mother's location after travelling for 110 miles.

She is  traveling to visit her grandparents who live 125 miles away.

a.

She stops for lunch 2/3 of the way.

The distance she has travelled after she stopped for lunch can be calculated as follows:

distance in miles = 2 / 5 × 125

distance in miles = 2 × 25

distance in miles = 50 miles

b.

She enters the city where her grandmother lives after 110 miles.

Hence,

9 / 10 × 125 = 1125 / 10 = 112.5 miles

Therefore, she is less than 9 / 10 of her way there.

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Answer: 3 17/20 is bigger than 3 13/28

Step-by-step explanation:

2 ways:

1) Turn the fractions into decimal form.

13/28 = 0.464

0.464 + 3 = 3.464

17/20 = 0.85

0.85 + 3 = 3.85

2) Check which one is bigger

3.85 is bigger than 3.464 because the tenth place is bigger than the second number.

Second way:

1) Remove the 3s.

Both equations have three, so you could remove both sides three

3 13/28  ?  3 17/20

13/28 ? 17/20

2) Multiply both bottom expressions by itself.

(The numbers that its multiplying equals to 1. When multiplying a number by 1, it stays the same.)

13/28 * 20/20 = 260/560

17/20 * 28/28 = 476/560

3) Compare the fractions

260/560  ?  476/560

260/560  <  476/560

The number in the fraction is bigger

Answer:

No, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.

Step-by-step explanation:

Convert both mixed numbers into improper fractions:

[tex]\implies 3 \frac{13}{28}=\dfrac{3 \times 28+13}{28}=\dfrac{97}{28}[/tex]

[tex]\implies 3 \frac{17}{20}=\dfrac{3 \times 20+17}{20}=\dfrac{77}{20}[/tex]

The lowest common multiple of 28 and 20 is 140.

Therefore, multiply the numerator and denominator of each improper fraction by the same number to make both denominators 140:

[tex]\implies \dfrac{97 \times 5}{28 \times 5}=\dfrac{485}{140}[/tex]

[tex]\implies \dfrac{77 \times 7}{20 \times 7}=\dfrac{539}{140}[/tex]

Therefore, as 539 > 485:

[tex]\implies \dfrac{539}{140} > \dfrac{485}{140}[/tex]

[tex]\implies \dfrac{77}{20} > \dfrac{97}{28}[/tex]

[tex]\implies 3 \frac{17}{20} > 3 \frac{13}{28}[/tex]

Therefore, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.

In the picture there is a cylinder with height 5 inches and diameter 4 inches. The surface area of cylinder is 87.62.

Given that,

In the picture there is a cylinder with height 5 inches and diameter 4 inches.

The surface area of a cylinder is the area that is enclosed by the flat bases and the curving surface of the cylinder. The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.

The surface area of cylinder is 2πr²+2πrh

r is radius which is diameter/2

r=4/2=2

h is 5

Surface area of cylinder= 2πr²+2πrh

=2π×2²+2π×2×5

=8π+20π

=28π

=28×3.14

=87.92

Therefore, the surface area of cylinder is 87.62.

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Answer:290

Step-by-step explanation:

first look at the ones place it is greater than 4 so round up  

286 to the nearest tenth is 290.

Place value, which is related to a digit's location in a number, is the amount that each digit is worth.

Given:

The number is 286.

The digit in tenth place is 6.

And the number 6 is greater than the number 4.

And 6 > 4.

So, the number will round off to the nearest tenth.

6 becomes zero.

And the number left to 6 will increase by 1.

That means 8 + 1 = 9.

So,

286 to the nearest tenth is 290.

Therefore, 290 is the nearest ten of the required number.

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The answer to the given function is [tex]B(a)= a/6-9[/tex].

A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides. A trapezium's bases are its parallel sides, while its legs are its non-parallel sides.

Given :

[tex]A(b)= 12( b+9)/2[/tex]

where, A(b) is the trapezoid's area

and b is the other base value

On solving the above equation further we get ;

[tex]A= 6(b+9)[/tex]

[tex]A/6= b+9[/tex]

this implies we get;

b= [tex]A/6-9[/tex]

Now convert this into function notation we get

[tex]B(a)= a/6-9[/tex]

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Given the system of equations:

To solve it by substitution, follow the steps below.

Step 1: Solve one linear equation for x in terms of y.

Let's choose the second equation. To solve it for x, add 3y to each side of the equations.

Step 2: Substitute the expression found for x in the first equation.

Step 3: Isolate y in the equation found in step 2.

To do it, first, add 48 to both sides.

Then, divide both sides by 15.

Step 4: Substitute y by 5 in the relation found in step 1 to find x.

Answer:

x = -9

y = 5

or (-9, 5)

Also, you can graph the lines by choosing two points from each equation, according to the picture below.

The range of the equation of the function given as y = x^2 + 4x + 7 is y >= 3

The equation of the function is given as

y = x^2 + 4x + 7

Differentiate the function with respect to x

So, we have

y' = 2x + 4

Set the differentiated function to 0

So, we have

2x + 4 = 0

This gives

2x = -4

Divide by 2

x = -2

Substitute x = -2 in the equation y = x^2 + 4x + 7

So, we have

y = (-2)^2 - 4 x 2 + 7

Evaluate

y = 3

The leading coefficient is positive

This means that the vertex is a minimum

So, we have the range to be

y >= 3

Hence, the range is y >= 3

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If the second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. The number of  phone calls did she receive each evening is: 30, 80, 20.

Let x , y, z represents the 1st , 2nd, and 3rd evenings respectively

X + Y + Z = 130

Y = 4Z  

X = z+10

Substituting the second and third equations into the first:

z+10 + 4z + z = 130

Combine like terms

6z + 10 = 130

Subtract 10 from both sides

6z +10 -10 = 130 -10

6z =130 -10

6z =120
Divide both side by 6z

z = 120/6

z = 20

Solving for y

y = 4z

y = 4×20

y = 80

Solving for x

x = z+10

x = 20 +10

x = 30

Check:

x + y + z =130

30 +80 + 20 =130

Therefore they each received 30 phones, 80 phones and 20 phones.

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Ms. Lantz would need to finish in 50.28 minutes to be eligible for the Houston Marathon.

The relationship between a score and the mean over a set of scores is simply quantified by a Z-Score, which is a measurable statistic.

A Z-score can explain to a trader why a value is unusual or average for a given set of data.

A Z-score below 1.8 suggests that a company is on the verge of bankruptcy, while a score closer to 3 shows that the company is doing well financially.

Solution:

The z-score is calculated using the formula: 

z = (x - μ)/σ

μ = Sample's average

σ = Sample's standard deviation

The values are as follows:

μ equals 57 minutes.

σ = 8 minutes

Probability equals 20%, or 0.20.

Determine the z-score for 0.20 using the negative z-table.

Z score is -0.84.

To find x, enter the values into the z formula.

z = (x - μ)/σ

-0.84 = (x - 57)/8

Simplifying;

x = -6.72 + 57

x = 50.28 minutes

Thus, Ms. Lantz would need to complete the Rocket Run 5k in 50.28 minutes in order to be eligible for the Houston Marathon.

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Answer:   The graph is below

======================================================

Explanation:

If x = 0, then,

g(x) = -x+1

g(0) = -0+1

g(0) = 0+1

g(0) = 1

Therefore, x = 0 leads to y = 1. The point (0,1) is on the g(x) line.

Now try x = 1

g(x) = -x+1

g(1) = -1+1

g(1) = 0

The point (1,0) is also on the g(x) line.

Draw a line through the points (0,1) and (1,0)

Then erase the portion that is to the left of x = -4

This is because g(x) is only graphed when x > -4; i.e. we're only graphing stuff to the right of x = -4.

We'll have an open hole when x = -4 since we aren't including it as part of the graph.

See below.

Step-by-step explanation:

5 people went on the Carowinds trip.

Answer:

C.

Step-by-step explanation:

as M is right over the middle of LN, this is an isoceles triangle (both legs are equally long).

so, we need to calculate only one leg and then double it fit both legs.

we get e.g. LM via Pythagoras.

LM is the Hypotenuse of the right-angled triangle with half of LN and the height to M being the legs.

so,

LM² = height² + (LN/2)² = 3² + 6² = 9 + 36 = 45

LM = sqrt(45) = 6.708203932... units

the perimeter is the sum of all 3 sides :

LN + LM + MN = LN + 2×LM = 12 + 2×sqrt(45) =

= 25.41640786... units

Answer: (0,3)

Step-by-step explanation:

The y-intercept for f(x)=x would be (0,0). Therefore, if we translate it up by three to get g(x), then the y coordinate would go up by 3, resulting in (0,3).

Mapping diagram (D) is not a function.

So, an option which is not a function:

Therefore, mapping diagram (D) is not a function.

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The bulb is 5 inches far from the vertex of the cross section.

A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the conic figure.

The standard equation for a parabola is typically expressed as y² = 4ax if the directrix is parallel to the y-axis, and y² = 4ax if the parabola is in the negative quadrants. The conventional equation of a parabola is x² = 4ax if the parabola is sideways, or if the directrix is parallel to the x-axis. If the parabola is in the negative quadrants, the equation is x² = 4ax.

Given, The equation x = 1/20y² can be used to model the cross section of a parabolic spotlight (with units in inches).

We must determine the distance between the bulb and the cross section's vertex.

Equation x = 1/20y² is alternatively denoted by the expression y² = 20x.

Now, comparing the equation to the parabola's conventional form, y²=4ax

So, 4a=20

a=5

Consequently, a=5 represents the distance from the cross section's vertex to the bulb.

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Given

Scale Factor of 2:7

When the scale factor is a:b

Recall the following

Given that the ratio is is 2:7 then we have the following

Answer:

c. 250 miles

Step-by-step explanation:

[tex]d=(50)(5)=250[/tex]

Answer:

The percentage change is 15%

Step-by-step explanation:

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If the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.

Temperature at midnight = 13 °

Temperature drop per hour = 2 °

We need to find the temperature at 3:00 AM

Number of hours till then = 3 hours.

Temperature drop will be calculated by using multiplication.

Temperature drop = 2 × 3 = 6°

Temperature ate 3:00 AM = 12 - 6 = 6°

Therefore, we get that, if the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.

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